A new study in Physical Review B reveals that popular quantum algorithms like VQE and QPE face massive scaling issues.
One of the biggest promises of quantum computing is the ability to simulate molecules with unprecedented accuracy. If quantum computers could do this efficiently, this may speed up the discovery of new medicines, batteries, and fertilizers.
However, a new theoretical study suggests that the road to this promise is much longer than many researchers had hoped. Through their analysis, the study authors show that even the most popular quantum algorithms face serious obstacles when trying to compute the lowest energy state of molecules—a fundamental quantity needed to understand chemical reactions.“Quantum chemistry is envisioned as an early and disruptive application for quantum computers. Yet, closer scrutiny of the proposed algorithms shows that there are considerable difficulties along the way,” the study authors note.Fragile algorithms meet noisy quantum hardwareThe researchers examined what it would take for quantum computers to achieve a real advantage in molecular simulations. Specifically, they focused on the problem of finding a molecule’s ground state energy, which is basically the lowest possible energy configuration of its electrons. Knowing this value helps scientists predict chemical stability and reaction pathways.To test the feasibility of quantum methods, the team analyzed two major algorithms used in quantum chemistry calculations: the variational quantum eigensolver and quantum phase estimation . Each algorithm targets a different generation of quantum hardware and comes with its own strengths and weaknesses.The first method, VQE, is designed for near-term quantum computers that are still noisy and prone to errors. VQE works through a hybrid approach where a quantum computer prepares a candidate quantum state for the molecule, while a classical computer adjusts parameters step by step to minimize the calculated energy. The idea is to gradually approach the molecule’s true ground state.However, “We find that decoherence is highly detrimental to the accuracy of VQE and performing relevant chemistry calculations would require performances that are expected for fault-tolerant quantum computers, not mere noisy hardware, even with advanced error mitigation techniques,” the researchers said.The problem becomes even more severe as molecules grow larger. For instance, when the researchers examined the chromium dimer molecule , they found that just one iteration of the VQE calculation could take about 25 days. When the many required optimization steps are included, the total runtime could stretch to around 24 years.Another challenge appears when dealing with strongly correlated molecules, where electrons interact in complex ways. Such systems often include transition metals and are considered important targets for quantum computing because they are difficult for classical simulations. However, the study shows that VQE frequently struggles to handle them accurately.The problem with quantum phase estimationThe second algorithm analyzed, QPE, is designed for future fault-tolerant quantum computers that can correct their own errors. In theory, QPE can determine energy levels with extremely high precision. However, it has a different challenge.QPE requires an initial quantum state that closely resembles the molecule’s true ground state. If the starting guess is poor, the probability of obtaining the correct answer becomes very small.The researchers found that this problem becomes dramatically worse as molecules grow larger due to a phenomenon known as the orthogonality catastrophe. As the number of particles increases, the overlap between the prepared input state and the true ground state shrinks exponentially. Since QPE’s success depends on this overlap, the probability of correctly measuring the ground state energy also drops exponentially with system size. To resolve this issue, the team developed a criterion that estimates the overlap between the prepared input state and the true ground state using the energy and energy variance of the initial state. By applying this framework to input states produced by advanced classical chemistry methods, they showed that the overlap consistently decreases exponentially as molecular size increases.This means that even if a fault-tolerant quantum computer becomes available, QPE could still struggle with large molecules because the chance of successfully extracting the correct energy becomes vanishingly small.Classical still beats quantumThese results highlight that classical computational chemistry methods remain surprisingly competitive, and in some cases could outperform quantum approaches, even with perfect quantum hardware.“These observations may also suggest that ground state estimation in chemistry may not be the most appropriate target for quantum computers. Besides the issues of quantum processors, we outlined in this paper, this statement is also due to the comparatively good quality of classical state preparation methods,” the study authors explained.However, the study does not rule out progress. Advances in fault-tolerant quantum hardware, improved state-preparation methods, and more efficient algorithms could eventually overcome some of the barriers identified. For now, however, the research serves as a reality check. Achieving a true quantum advantage in chemistry will likely require breakthroughs in both hardware and algorithms before quantum computers can surpass classical machines on these fundamental molecular calculations.The study is published in the journal Physical Review B.
Physics Quantum Computing Quantum Physics
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